Corpus ID: 214795326

Past and recent contributions to indefinite sublinear elliptic problems

@article{Kaufmann2020PastAR,
  title={Past and recent contributions to indefinite sublinear elliptic problems},
  author={U. Kaufmann and Humberto Ramos Quoirin and Kenichiro Umezu},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
  • U. Kaufmann, Humberto Ramos Quoirin, Kenichiro Umezu
  • Published 2020
  • Mathematics
  • arXiv: Analysis of PDEs
  • We review the indefinite sublinear elliptic equation $-\Delta u=a(x)u^{q}$ in a smooth bounded domain $\Omega\subset\mathbb{R}^{N}$, with Dirichlet or Neumann homogeneous boundary conditions. Here $0<q<1$ and $a$ is continuous and changes sign, in which case the strong maximum principle does not apply. As a consequence, the set of nonnegative solutions of these problems has a rich structure, featuring in particular both dead core and/or positive solutions. Overall, we are interested in… CONTINUE READING

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